We present new CO(2-1) observations of 3 low-z (~350 Mpc) ULIRG systems (6 nuclei) observed with ALMA at high-spatial resolution (~500 pc). We detect massive cold molecular gas outflows in 5 out of 6 nuclei (0.3-5)x10^8 Msun. These outflows are spatially resolved with deprojected radii of 0.25-1 kpc although high-velocity molecular gas is detected up to ~0.5-1.8 kpc (1-6 kpc deprojected). The mass outflow rates are 12-400 Msun/yr and the inclination corrected average velocity of the outflowing gas 350-550 km/s (v_max = 500-900 km/s). The origin of these outflows can be explained by the nuclear starbursts although the contribution of an obscured AGN can not be completely ruled out. The position angle (PA) of the outflowing gas along the kinematic minor axis of the nuclear molecular disk suggests that the outflow axis is perpendicular to the disk for three of these outflows. Only in one case, the outflow PA is clearly not along the kinematic minor axis. The outflow depletion times are 15-80 Myr which are slightly shorter than the star-formation (SF) depletion times (30-80 Myr). However, we estimate that only 15-30% of the outflowing gas will escape the gravitational potential of the nucleus. The majority of the outflowing gas will return to the disk after 5-10 Myr and become available to form new stars. Therefore, these outflows will not likely quench the nuclear starbursts. These outflows would be consistent with being driven by radiation pressure (momentum-driven) only if the coupling between radiation and dust increases with increasing SF rates. This can be achieved if the dust optical depth is higher in objects with higher SF. The relatively small sizes (<1 kpc) and dynamical times (<3 Myr) of the cold molecular outflows suggests that molecular gas cannot survive longer in the outflow environment or that it cannot form efficiently beyond these distances or times. (Abridged)
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